D.Ed. / The study focused on the placement of Grade 10 learners in either Mathematics or Mathematical Literacy. The purpose was to develop guidelines to assist Grade 10 learners to make a proper choice, which would render their placement more justifiable and objective and, in turn, enhance their results. A central theme of the National Curriculum Statement (NCS) is the importance that secondary schools will shape learners to become responsible citizens in a fast-developing, scientific and technological society. South Africa has an urgent need for more scientists, engineers, high-level economists and technicians, which can only be satisfied if learners with potential for science-related studies are identified. Due to the fact that learners need skills to interact critically with the world outside the school environment, more learners should be encouraged to take Mathematics. A good foundation of Mathematics and Mathematical Literacy necessitates the development of guidelines to add value to assessment. Therefore, this study examined the nature of Mathematics and Mathematical Literacy, the historical background of Mathematics education in South Africa, constructivism and its approaches to learning and teaching, as well as cognitive and non-cognitive factors associated with achievement and general test evaluations. A pragmatic philosophy was followed. National Curriculum Statement (NCS) documents were analysed to distinguish between Mathematics and Mathematical Literacy in terms of subject content. Qualitative and quantitative information was collected by means of interviews and questionnaires respectively.The analyses of the NCS documents showed content similarities and differences between Mathematics and Mathematical Literacy and identified the gaps in learners’ learning experiences that could contribute to non-achievement in either subject.

M.Ed. / The method used in the classroom is thought to have an effect on the learners learning the purpose/use of mathematics in their environment. Many see mathematics as a set of signs and symbols that are meaningless in their lives. The manner, in which mathematics is taught in the classroom, extends the thought of learners in believing that mathematics is a compulsory learning area that is required to be passed in order for them to proceed to the next grade. Meanwhile, the learners may be oblivious to the contribution mathematics can make in their lives. One of the major contributory factors for this kind of thought is that mathematics is not taught in a way that helps learners understand its purpose/use in society. Thus, meaningless learning is perpetuated because of the approach in the classroom. If educators could alter their methodology in the classroom, then learners would be able to make sense of the subject and so apply the knowledge in their environment when the need arises. One of the ways to do this is to ensure that educators engage in meaningful and relative teaching. The research for this study was based on the questionnaire and observation instruments. The target was primary school learners from grades five, six and seven, who were required to answer a closed questionnaire based on their understanding of the relevance of mathematics to their environment. The aim was to see how the educators’ methodology affected the learners’ understanding of mathematics. Educators were also given questions along the same lines, with their lessons observed and observations recorded, according to an observation protocol. The conclusion that the researcher reached was that learners were not taught in a purposeful manner that might assist them in understanding and applying mathematics to their environment. Whatever they learnt or were taught in the classroom was in isolation, that is, there was minimal, if any, integration into other learning areas. One possible solution to this problem can be that the educators need to change their teaching strategies. Some of the possible strategies that they could use are cooperative learning, problem solving, the constructivist approach to teaching or an amalgamation of more than one strategy to obtain the outcomes. In effect, if learners are made to realize the relevance of mathematics consciously; their mindset towards learning it will be more welcoming and accepting of it. Understanding forms the foundation for application, and therefore if the problems in the classroom relate to the learners’ experiences in their environment, then mathematics becomes meaningful to them and in turn becomes usable.

Over the past decade, a sizeable body of research has addressed issues in metacognition, the way in which the learner plans, implements and monitors cognitive behavior (Garofalo and Lester, 1985). This type of consideration is of interest to studies which try to build models of human cognitive process for such applications as artificial intelligence and/or curriculum development. To form one's own mental map of a body of knowledge is to discover a structure of, or to impose a structure on, that body of knowledge. In the case of secondary school mathematics curricula, the student is typically discovering structure which is to some degree made explicit in the presentation of the material. However, when the language of instruction is not the student's first language, when the student is unaccustomed to many of the communication conventions of the language of instruction and of the subject register as well, fewer assumptions can be made about how the student is navigating around the body of knowledge. In this study, the relatively scarce questions asked by ESL (English as a Second Language) students in a secondary school English-speaking mathematics classroom were observed over time. The data provide some evidence of the natural manner in which the students attempt to form a mental map of the body of knowledge under exploration. The body of research on classroom questions (e.g. Sinclair and Coulthard, 1975) has focused almost entirely on questions asked by the teacher. Questions asked by students differ in both form and intention from questions asked by teachers, however; as a result the methods of analysis employed in studies of teacher questions are inappropriate for the analysis of student questions. A more appropriate method of analysis for this study's examination of student questions about a body of knowledge was found to be an ethnographic one which regarded questions as a means of eliciting aspects of a structured knowledge domain. Mohan's (1986) knowledge framework, which embodies a structured taxonomy of topics and tasks, is used here to categorize the data according to the type of knowledge sought through each student question. Observed differences between the surface content of student questions and the context-apparent intention of these questions provide some insight into how students may be assisted to better ask the questions which they use to seek help in their navigation of bodies of knowledge. Published teaching materials intended for ESL students of secondary mathematics are examined here for relevance to the students' need to develop help-seeking strategies; suggestions for more effective accommodation of this need are made. Computer software developed by the researcher for exploration of possibilities in computer aided instruction in question formation is described. / Education, Faculty of / Language and Literacy Education (LLED), Department of / Graduate

The purpose of this investigation was to examine, through the use of survey data, relationships between inputs of schooling and outcomes, as measured by student achievement in mathematics. The inputs of schooling were comprised of a number of variables grouped under each of the following categories: students' and teachers' backgrounds; students' and teachers' perceptions of mathematics; classroom organization and problem-solving processes. Outcome measures included student achievement on test total, problem solving and applications. A related question involved exploration of the appropriateness of using cross-sectional survey data to make decisions based on the relationships found among the input and output variables. To address this question, results from a subsequent longitudinal study, which utilized the same instruments, were examined first with post-test data and second with the inclusion of pre-test data as covariates. Data collected from teachers and students of Grade 7 in the 1985 British Columbia Assessment of Mathematics were re-analysed in order to link responses to Teacher Questionnaires with the students' results in teachers' respective classrooms. Responses were received from students in 1816 classrooms across the province and from 1073 teachers of Grade 7 mathematics. The data underwent several stages of analysis. Following the numerical coding of variables and the aggregation of student data to class level, Pearson product-moment correlations were calculated between pairs of variables. Factor analysis and multiple regression techniques were utilized at subsequent stages of the analysis. A number of significant relationships were found between teacher and student behaviors, and student achievement. Among the variables found to be most strongly related to achievement were teachers' attitudes toward problem solving, the number and variety of approaches and methods used by teachers, student perceptions of mathematics, and socio-economic status. Results also show that student background, students' and teachers' perceptions of mathematics, classroom organization and problem-solving processes all account for measurable variances in student achievement. The amount of variance accounted for, however, was higher for achievement on application items, measuring lower cognitive levels of behavior, than on problem-solving items which measured cognitive behavior at the critical thinking level. Through examination of the standardized beta weights from the cross-sectional and longitudinal models, it was found that prediction of change in achievement based on corresponding change in classroom process variables was similar for both models. Differences, however, were found for variables in the other categories. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

M.Ed. (Subject Didactics) / Each child has his own personality and individuality. Children are learning in different ways, at different tempo's and achieve different heights of success with.their efforts. The degree to which the learner is able to master new concepts, is closely related to the reference framework and given pre-knowledge. However, the learning process is not always successful. Various reasons for this phenomena can be identified. This study focuses on the role which misconceptions play in this regard. In general, misconceptions can be defined as a distortion or misinterpretation of the learned concepts. synonyms used to describe this phenomena includes words. like "previous knowledge", "preconceptions" and "alternative frameworks" Misconceptions in Mathematics are numerous. In various studies conducted, misconceptions were identified in almost all areas of Mathematics. Likewise a great deal of misconceptions were found existing among students concerning the handling of fractions. It is an impossible task to research all misconceptions in Mathematics in one study. For this reason it was decided to do research on only one aspect, namely fractions where possible misconceptions can occur. With the empirical research which was conducted, certain misconceptions in the area of fractions were identified. These misconceptions include, amongst other, the following: 1. The sum of and difference between two fractions. There is very little or no notion of the smallest denominator. 2. Multiplying and division of fractions. The student is uncertain about the role which the numerator and the denominator play in the solution. As fractions play such an important role in Mathematical success, it is suggested that a plan of action will be set as soon as possible in order to prevent misconceptions influencing the student learning process.

Please read the abstract in the section 00front of this document / Thesis (PhD)--University of Pretoria, 2006. / Humanities Education / PhD / Unrestricted

In the catalog issue of the Bulletin of Florida State University, to be published sometime during 1950, will appear a challenging innovation: the General Education course in mathematics, titled mathematics 105, will be listed under the general area of Communication through Language. This, so far as the writer is able to ascertain, will be the first time a course in mathematics has been so listed in any university catalog. It will be the purpose of this paper to examine some aspects of the historical development of mathematics to justify such a classification and to explore some of the implications of such an approach for the teaching of mathematics. / Typescript. / "July, 1950." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Includes bibliographical references (leaves 26-30).

The results reported here are the product of the research titled: Using history in the teaching of mathematics. The subjects are students in two classes of algebra II course at Florida State University High School-- 36 students-- makes and females whose ages are mostly 18 and a few 17 and 16 years old. Algebra II is a course that is usually taken by high school seniors in 12th grade and a few 11th or 10th grade students which explains why the ages of the students are mostly 18 and a few 17 and 16 years old. In this investigation, both quantitative study and qualitative study were employed. The quantitative study was the main study-- a teaching experiment using quasi-experimental methodology that involves two groups-- group 1 and group 2. Group 1 is the control group, where various algebraic/mathematical concepts, or topics were taught or explained to students with the necessary formulas. Group 2 was the experimental group in which the accounts of the historical origin of algebraic/mathematical concepts and the mathematicians (Lewis Carroll, Archimedes, Pythagoras, and Sophie Germain) who brought forward or created the concepts were used to augment pedagogical lessons and exercises used for this study as the main feature of pedagogy. The qualitative study augmented the main quantitative study; it was a follow-up interview for students to probe further an in-depth rationale for the research theme, using history in the teaching of mathematics. The statistical analysis results indicated that there is a significant difference in the mean of score for the control group students and the mean of scores of the experimental group is greater than the mean on scores of student's performance in the control group; and the interview questions responses indeed corroborate the fact that the use of history in teaching mathematics does improve learning and understanding of algebraic/mathematical concepts. / Typescript. / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisors: Elizabeth Jakubowski, Herbert Wills III, Professors Co-Directing Dissertation. / Includes bibliographical references (leaves 202-205).

A research report submitted to the Wits School of Education, Faculty of Humanities, University of the Witwatersrand in partial fulfilment of the requirements for the degree of Master of Education by combination of coursework and research / Percent is a familiar, yet complex topic that is found to be difficult for both adults and children. The question of why percent has been persistently difficult has spurred much research, the most notable of which was conducted in the early 1990’s. Those studies have adopted a cognitive perspective. This study adds a commognitive perspective to the discussion by proposing a model for the development of percent discourse (PD-Model). The model rests on Sfard’s premise that learning mathematics is synonymous with modifying and extending one’s discourse. I begin by employing a cognitive framework of percent for the design of written tests to identify the areas of percent that first-year university students experience difficulty with. The quantitative analysis of the written tests shows that less than half the students obtained a score of 50% or more. Later, in search of the features of students’ discourse that hinder their access to percent discourse, I examine the discourse of two pairs of students in interview sessions. I illustrate the application of the PD-Model as an interpretive analytical tool that offers an explanation for the insufficiency in their objectification of percent as a comparative ratio. This study confirms the results of Parker’s (1994) study, that is: percent is difficult for students to work with. The key findings of the discursive analysis show that students’ discourse of percent is narrow and deeply rooted in a percent-as-fraction notion. The students’ discourse is predominantly additive in nature and does not show signs of recognising the underlying multiplicative structures of percent tasks. As such, a fully-fledged objectification of percent as a comparative ratio is not evident in the students’ discourse of percent. / NG (2020)

Research Report submitted to the School of Education,Faculty of Humanities, University of the Witwatersrand, Johannesburg In partial fulfillment of the requirements For the degree in Master of Education (Inclusive Education) July 2019 / NG (2020)